Performing statistical timing analysis with non-separable statistical and deterministic variations

Abstract

In one embodiment, the invention is a method and apparatus for performing statistical timing analysis with non-separable statistical and deterministic variations. One embodiment of a method for performing timing analysis of an integrated circuit chip includes computing delays and slews of chip gates and wires, wherein the delays and slews depend on at least a first process parameter that is deterministic and corner-based and a second process parameter that is statistical and non-separable with the first process parameter, and performing a single timing run using the timing quantity, wherein the single timing run produces arrival times, required arrival times, and timing slacks at outputs, latches, and circuit nodes of the integrated circuit chip. The computed arrival times, required arrival times, and timing slacks can be projected to a corner value of deterministic variations in order to obtain a statistical model of the delays and stews at the corresponding corner.

Description

BACKGROUND OF THE INVENTION[0001]The present invention relates generally to design automation, and relates more particularly to the timing analysis of integrated circuit (IC) chips.[0002]Manufacturing and environmental variations are unavoidable in integrated circuit (IC) chips. Delays and slews of signals propagated through logic gates and wires depend on these variations. Statistical timing is commonly used to analyze IC chips for timing violations in the range of these variations. Statistical timing assumes that manufacturing and environmental variations are random and therefore behave statistically. Applying this assumption, statistical timing analysis models chip timing statistically. It approximates timing accurately in the regions of highly probable values of variations while allowing higher error in the regions of less probable values of variations.[0003]Conventionally, the delays of gates and wires in the chip are modeled in the linear canonical form of variational paramete...

AI Technical Summary

Problems solved by technology

Manufacturing and environmental variations are unavoidable in integrated circuit (IC) chips.

Some variables, however, are not separable and thus do not interact linearly.

Moreover, variables like supply voltage are not statistical, but deterministic.

The statistical approximation used by statistical timing analysis is not accurate enough to model variations of supply voltage or similar deterministic parameters.

The statistical approximation cannot achieve sufficient accuracy near the corner values of the deterministic parameters, especially if some statistical parameters are not separable with the deterministic parameters.

The use of multiple timing runs, however, is inefficient and inconvenient.

For instance, timing closure will take longer and will require more computational resources.

Additionally, a circuit optimized at one supply voltage will often fail at another supply voltage.

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